2.5 cold readout electronics
2.5.2 multiplexer chips
The version MUX07a multiplexer chips used in theBicep2 focal plane are described in more detail
in this section. The DC SQUIDs are a planar washer design with high coupling efficiency to the input and feedback coils. The SQUID loop is wound in a cloverleaf pattern to create a second-order gradiometer. The inductance is placed entirely on one leg of the loop to create an asymmetric V−Φ
curve with two unique lock points.
of the self-inductance is placed on one branch and all of the bias current flows in one direction around the SQUID. The corresponding imbalance in the self-induced flux in the loop causes a distortion in the V−Φ response of the SQUIDs. There is an increase in the slope on one side of the curve and
a decrease on the other.12 This allows for two different lock points on the SQUID, one with higher
gain and dynamic resistance and the other with lower gain and dynamic resistance, but longer flux base line.
The planar washer SQUID design allows for the input and feedback coils to be deposited directly above the SQUID loop for high coupling efficiency [31]. This arrangement leads to resonances in the SQUID V−Φ response, which are mitigated by the use of intracoil damping resistors [27]. Each
turn of the feedback or input coils is shunted by a∼1 Ω resistor to alter the resonant frequency of
the circuit. Resonances create low-gain lock points on the SQUIDs, which is undesirable for high amplifier gain and low and stationary noise. Despite the damping resistors, the SQ1s used inBicep2
showed pronounced resonances, which required careful selection of the SQ1 biases and lock points (§4.1.8.2).
A mutual inductance naturally exists between the feedback and input coils due to their colocation. As the current in the common feedback line is switched from row to row this mutual inductance induces screening currents in the superconducting input transformer coils of all SQ1s in the same column. This in turn induces screening currents in the input coils of all the other TES bias circuits. The current in the superconducting transformer is persistent, but the TES circuits include resistance and so their flux response decays with the L/R time constant of the circuit. This flux decay modulates the transformer currents, thereby inducing a decaying input flux in each of the SQ1s. This is a potential crosstalk source between all channels in the same column (§4.2). To prevent this, a second
set of input and feedback coils are wound in the opposite direction. Thus, screening currents induced in one coil by the other are nulled by the same currents generated in the second set of coils. To
12The same effect occurs when the Josephson shunt resistors are asymmetric or using additional positive feedback (APF) [14].
match the mutual inductance of the SQUID loop and coils as closely as possible, the second set of coils are wound around a dummy SQ1. This dummy SQ1 is unbiased and only serves to match the geometry of the functional SQ1 as well as possible. The SQ2 does not have a dummy SQUID, so a higher coupling coefficient exists between its feedback and input coils. The dummy SQ1 effectively reduces the coupling coefficient kf b−in between the feedback and input coils. NIST measured a
reduction fromkf b−in'0.6 tokf b−in'1.6·10−2with the introduction of the dummy SQ1 [16].
Newer versions of the multiplexer chips, including the MUX07a, use a double-transformer input coil [17]. In addition, the MUX07a and older versions used a half-integer number of windings for the input coil and feedback coils around the SQUID loop. The input and feedback coils are wound around the cloverleaf SQUID loop with 1.5 turns for SQ1 and 4.5 turns for SQ2. Since the input coils of both stages are coupled to transformer loops, an increase in the effective area (Aef f = Φs/∆B)
of the SQUIDs has been measured compared to older designs that don’t include transformers [58]. The superconducting transformer loops generate screening currents for flux threading the loop that couples to the SQUIDs. The half-integer windings around the lobes of the cloverleaf leave a portion of the loop unshielded outside of the lobes of the SQUID loop. The measured effective areas of SQ1 and SQ2 for the MUX07a are 883µm2and 483µm2, respectively. The earlier MUX06a version, had
a factor of∼180 lessAef f for SQ1 and the sameAef f for SQ2, since it used an input transformer on
SQ2 but not SQ1. Beginning with version MUX09a, NIST now uses whole-integer windings of the input and feedback coils around the gradiometer lobes. Now the SQ1 has two windings as opposed to 1.5 and the SQ2 has four windings as opposed to 4.5. TheAef f has been reduced by a factor of ∼1471 and∼22 for SQ1 and SQ2, respectively.
One of the SQ1s on every column is not connected to a TES and its input coil is left open. This “dark” SQ1 has been designed to allow the removal of a common-mode signal from the other 32 channels in the column. This is potentially useful for reducing a common-mode low-frequency noise contribution of the SQUID multiplexer [16]. Due to inductive pickup between the input coils of the SQUIDs, the dark SQ1 is placed next to the SQ2. This prevents TES signals in the SQ1 input coil from coupling to all other channels in the column through the SQ2 (§4.1.5.1).
2.5.3
series arrays
The final stage of the multiplexer is an array of 100 series SQUIDs, as explained in§2.5.1.2. Each
100-element SSA is lithographically fabricated on a single chip. Eight SSA chips are packaged to- gether in a module that supports the chips, routes their electrical connections and provides magnetic
The SQ2 to SSA circuit was believed to be the lowest pole in the amplifier and thus dominating the settling time. This in turn limits the readout rate of the detectors with a corresponding increase in the aliasing of out-of-band detector and readout noise. The Bicep2 TESs have an excess noise
plateau that extends to 10 kHz and requires a high readout ratefnyq &10 kHz to avoid significant
aliased noise. Thus, the SQ2 to SSA circuit has been optimized for maximum bandwidth. The SQ2s are biased on the higher dynamic resistance lock point for a lower L/R time constant. The SQ2–SSA cables are shortened as much as possible to reduce the parasitic inductance. The largest contribution to the inductance in that circuit is the SSA input coil inductance (Lina). At the time
of theBicep2 deployment, SSAs were available with either 1-turn or 3-turn input coils. The 3-turn
coils give higher coupling and gain for the SQ2 output to the SSA, which decreases the input-referred amplifier noise. The increased inductance leads to longer settling times and lower readout rate. The increased amplifier noise is offset by the much larger decrease in aliased noise. In the end, the settling time measurements between the 1-turn and 3-turn input coils were inconsistent and 3-turn arrays were used.
2.5.4
Nyquist chips
The Nyquist interface chips low-pass filter the detector signal and provide bias resistors for the TESs.
TheBicep2 focal plane uses 16 version NYQ09a chips. Each chip can service 33 TES bias circuits,
but one of the circuits is left open to provide a diagnostic dark SQ1.
The detector signals are low-pass filtered prior to being sampled at the frame rate by the mul- tiplexer. A single-pole, low-pass filter is created from the L/R circuit from the detector operating resistance in series with a total inductanceLtot= 1.6µH. The Nyquist chips includeLN yq= 1.35µH
inductors with an additional inductanceLin = 0.25µH from the SQ1 input coils. The TESs were
designed to operate at Rtes = 30 mΩ, so the bandwidth of the TES circuit, excluding ETF, is
bondpads to MUX chip
bondpads to TES lines bondpads to
TES bias lines
shunt resistor gradiometric inductor gradiometric inductor
~
~
to next detector cell~
~
Figure 2.19: An image of a Nyquist interface chip and the interface circuit for one TES. Left: A micrograph of a NYQ chip showing the circuit elements and wire bonds for two-and-a-half detector cells. This is an older version of the Nyquist chip with a lower inductance value. Right: A schematic describing the circuit elements seen in the micrograph for one of the detector cells. Each cell includes a 3.0 mΩ resistor, a gradiometric 1.35µH inductor separated between the two input lines,
superconducting microstrips and bond pads. The microstrips are shown in red where one crosses without making connection to the other. Note that the first circuit cell on the left is generally left open input for the dark SQ1.
fromτel. High in the transition, where the poles are well separated, this is a reasonable approxima-
tion.
The inductive elements are rectangular spiral inductors wound from niobium microstrip. The total inductance is split between two spiral inductors, which are wound in opposite directions to create a first-order gradiometer that rejects ambient fields but is sensitive to their gradient. There are additional microstrips that cross over the windings to connect to the center termination of the inductor. The inductors are deposited above a niobium ground plane with square holes in the center. This geometry ensures balance of the gradiometer by the focusing of flux through the washer center due to the Meissner effect. The inductance is determined by the number of windings. Due to space constraints on the chips, the size of the ground plane limits the inductance to 1.35µH.
Higher inductance chips can be fabricated with the same form factor, but the ground plane must be eliminated.
The choice of inductance on the NYQ chips is a balance between aliasing of noise and detector stability. For an ideal detector a single-pole filter with f3dB = 3 kHz should provide readout rea-
sonably free of aliased noise for fsample &6 kHz. The high-frequency excess noise plateau of the
bias optimization and crosstalk (§4). The shunt resistors were confirmed to be 3.0 mΩ in separate
four-wire measurements conducted at∼300 mK.
2.5.5
electrical routing
The cold electronics are distributed between the ∼ 300 mK focal plane and a circuit board that
is sunk to the 4 K base plate. Superconducting niobium-titanium, twisted-pair cables connect the focal plane and 4 K circuit boards, terminating on either end in 37-way MDM connectors. There are six cables that connect to the focal plane. Two cables each provide 32 wires needed for the bias and flux bias for the SQ2s on eight multiplexer chips. Two additional cables provide 32 wires for the SQ1 flux bias and TES bias on eight chips. The remaining two cables provide the 66 wires needed for the SQ1 bias, with 34 channels on one cable and 32 on the other.
Two circuit boards are mounted to the 4 K base plate near the fridge. They break out and heat sink electrical connections leading to the cryostat feedthrough, break out and heat sink the series array modules, and provide mounting points for the SQ2 bias resistors. The circuit boards are manufactured by Murietta circuits. Two boards are used, each containing a series array module, eight SQ2 bias resistors, two 100-way MDM connectors, and two 37-way MDM connectors for the bias and flux bias cables. One of the boards is used to break out the wiring for the SQ1 bias lines and includes two additional 37-way connectors.
Shielded, isothermal 100-way cables connect the 4 K boards to three 100-way pi-filtered con- nector modules that feed the cables through 4 K base plate of the insert (§2.6). Three additional
shielded, isothermal 100-way cables connect the modules to the hermetic cryostat feedthrough. The feedthrough is made from circuit boards epoxied into an aluminum plate that bolts to the cryostat wall, and is equipped with 100-way MDM connectors on both sides.
2.6
shielding
The TESs and SQUIDs are sensitive to magnetic fields and must be adequately shielded. SQUIDs are the most magnetically sensitive device in the instrument, by design. The planar SQUIDs are sensitive to fields applied normal to them. The gradiometric design of the SQUID loop and the SQ1 and SQ2 input transformers reject all but second-order spatial gradients in the field (δ2B
z/δxδy). Magnetic
pickup is dominated by the SQ1 input transformer in the MUX07a chips used in Bicep2 (§2.5.2).
Magnetic fields affect theTc,G, and the transition width andαof TESs. However, TESs are much
less sensitive to magnetic fields than SQUIDs. Both static and time-varying fields are problematic. Static differences in the flux across the series array SQUIDs can decrease the coherence and gain of the array. Spatial gradients and time-varying field fluctuations across the detector arrays can lead to variations in the TES parameters. Flux can be trapped in the superconductors during initial cool down and thermal cycling. The Lorentz force from time-varying fields or applied current can cause motion of the trapped flux, leading to increased noise. During observations scan-synchronous contamination is introduced by the changing attitude of the telescope and modulation of the local field by the ferromagnetic mount. Fluctuations that are common-mode for detectors are removed by pair-differencing or removal of a scan-synchronous template. However, differential fluctuations within a polarization pair will contaminate the polarization measurement.
The shielding requirements are set by the sensitivity derived for the TESs and SQUIDs and maximum desired contamination signal. If the contamination is limited to.100 nK the magnetic
field must be attenuated to<10 pT at the TESs and <0.1 pT at the SQUIDs of the MUX chips.
To attenuate earth’s 50 µT field to these levels the shielding factor must be∼7·106 at the TESs
and∼5·108 at the SQ1s.
The magnetic shielding has been designed to attenuate stray fields at the focal plane and the SSA modules without impeding the optics. In addition, precautions have been taken to prevent the use of ferromagnetic materials near the focal plane which might distort the local field. A combination of superconducting and high-permeability cryogenic shields are used to achieve high shielding factors. Superconductors shield by expelling flux through the Meisner effect, but trap flux in strong fields when it’s more energetically favorable than expelling it. The superconducting shields are all made of niobium, which has a critical temperature of 9.2 K. High-permeability materials effectively absorb nearby magnetic fields by pulling them into their bulk. Cryoperm1310 is a nickel-
iron alloy optimized for high-permeability at low temperatures. It is annealed for use at 4 K, has
This open-ended geometry gives the best performance for fields applied along the cryostat axis. The field component parallel to the axis is the least attenuated, while the component normal to the axis is most attenuated.
The next level of shielding is the superconducting niobium spittoon that surrounds the sub- Kelvin structure (§2.2.3). The focal plane is further shielded by a combination of high-permeability
and superconducting shields. These shields are especially important for reducing the field parallel to the cryostat axis, which is the field component the focal plane SQUIDs are sensitive to. The backshort is made of superconducting niobium and provides shielding for the MUX chips and the detector arrays (§2.4.7). A Metglas shield is used on the opposite side of the MUX chips from the
backshort to completely enclose them in magnetic shielding. Fifteen layers of 15 µm thick Metglas
2714A were bonded together and cut into crescent shapes that fit in a recess between the PCB and detector plate. The alternating layers of Metglas were crossed to prevent overlapping seams in the layers that might allow fringing fields. To prevent flux from being trapped in the superconducting shields the spittoon and focal plane are cooled from the center. This center-point cooling is intended to push trapped flux radially outward as the shields are slowly cooled.
Variations in the input flux of the series array SQUIDs must be carefully controlled. The output voltages of the SQUIDs add in series, so differences in the input flux will cause the signal to add out-of-phase and the gain of the array will be diminished. The series arrays are heavily shielded from external magnetic fields to prevent this. The SSA modules are surrounded by a Cryoperm sleeve that slides into a superconducting niobium box. An additional shield made of several layers of Metglas 2714A is wrapped around the niobium shield. As a further precaution the location and orientation of the arrays in the 4 K Cryoperm shield was optimized. The modules were installed so that the flux-sensitive axis of the SSAs is normal to the boresight axis. In addition, the modules were elevated off the base plate so they are located further from the ends of the magnetic shields of the cryostat.
Simulations were run in COMSOL Multiphysics to assess the magnetic shield design.15 The
simulations demonstrated that the 4 K Cryoperm shield would not saturate in a 50 µT ambient
field, so would perform adequately as the first-stage magnetic shield. They also showed that for a moderate scenario — the field applied 45◦ to the cryostat axis — the ambient field would be attenuated to ∼ 10 pT normal to the focal plane at the SQUIDs, with only a very small spatial
gradient. The ambient field would be attenuated to a total magnitude at the detector array of
∼50 nT, with a very small spatial gradient. The desired attenuation of the simulated shields did
not meet the ideal shielding requirements to limit fluctuations to .100 nK. However, any pickup that is common-mode in a detector pair will be rejected by pair differencing and scan-synchronous